nLab superoperator



Higher linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology



Paths and cylinders

Homotopy groups

Basic facts




In quantum physics and in particular in the context of quantum computing a linear map between spaces of linear operators (hence an “operator on operators”) is sometimes called a superoperator.

Notably density matrices representing quantum states are given by linear operators and a quantum operation is a superoperator that preserves the defining properties of density matrices. (Beware that sometimes different or no distinctions between “quantum operation” and “superoperator” are made.)

  • The Geometry of Interaction-construction is a genral abstract construction of a category of superoperators. See there for more.


  • Greg Kuperberg, section 1.4 of A concise introduction to quantum probability, quantum mechanics, and quantum computation, 2005 (pdf)

Created on January 20, 2014 at 15:47:21. See the history of this page for a list of all contributions to it.